Fate of turbid glacial inflows in a hydroelectric reservoir

Turbidity from glacial meltwater limits light penetration with potential ecological consequences. Using profiles of temperature, conductivity, and turbidity, we examine the physical processes driving changes in the epilimnetic turbidity of Carpenter Reservoir, a long and narrow, glacier-fed reservoir in southwest British Columbia, Canada. Following the onset of permanent summer stratification, the relatively dense inflows plunged into the hypolimnion, and despite the high glacial load entering the reservoir, the epilimnion cleared due to particle settling. Using a one-dimensional (longitudinal) diffusion equation for a decaying substance to describe the variation in epilimnetic turbidity, we obtain two nondimensional parameters: the epilimnetic inflow parameter, I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {I}$$\end{document}, a measure of the turbidity flux into the epilimnion; and the dispersion parameter, D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {D}}$$\end{document}, a measure of longitudinal dispersion. In the case of Carpenter Reservoir: I≪1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {I}\ll 1$$\end{document}, indicating that turbidity declines over the summer; and D≪1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {D}}\ll 1$$\end{document}, indicating a strong gradient in turbidity along the epilimnion. Using our theoretical formulation of epilimnetic turbidity variations in conjunction with monthly field surveys, we compute the particle settling velocity (∼0.25md-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sim}{0.25}\,{\hbox {m}\,\hbox {d}^{-1}}$$\end{document}), the longitudinal dispersion coefficient (50–70 m2s-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {m}^{2}\,\hbox {s}^{-1}}$$\end{document}), and the flux of turbid water into the epilimnion (∼1%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sim }1{\%}$$\end{document} of the total inflow). Our approach is applicable to other reservoirs and can be used to investigate changes in turbidity in response to changes in I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {I}$$\end{document} and D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {D}}$$\end{document}.